A joint probability distribution of invariants for all space groups

A probability distribution is derived in the form of an infinite sum of cosine phase invariants between any number of structure factors and is applicable to any space group. No approximations are made. With the use of only the first-order terms, and the assumption that the reflection magnitudes are small and that all atoms are equal, the distributions reduce to the known invariant distribution forms. The effect of neighbourhood reflections is implicit in the form of the distribution.